Városliget is where Pest stops being a city and becomes a park, and the whole thing was staged for the 1896 millennium — a thousand years since the Magyars arrived. The walk reads as one set-piece after another: a square, a castle, a lake, the baths. Three kilometres of parkland, best in the afternoon when the light is on the colonnade and the steam rises off the pools.
Start at Hősök tere, the Millennium column and its curved arcades; stand at the open end first to read the whole thing. The Museum of Fine Arts holds the square's north side and the El Grecos, if you want them. Then into the park to Vajdahunyad vára, the castle built as a stage set of borrowed Hungarian styles and kept because the city wouldn't let it be torn down.
The lake curls round the castle — boats in summer, skaters in winter. End at the Széchenyi fürdő (thermal bath), the yellow palace where the chess players sit in the steaming water. Go in if you've brought a towel; either way the M1 at the baths runs straight back down the avenue.